Length of the rectangle is .

Breadth of the rectangle is .

Area of the rectangle is .

.

Differentiate on each side with respect to .

Product rule of derivatives: .

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For maximum or minimum values eqaute the first derivative to zero.

use second derivative test to determine whether it is maximum or minimum.

Consider

Differentiate on each side with respect to .

.

Therefore rectangle has maximum area at .

Maximum area of the rectangle is square units.

(2)

Area of the rectangle is .

Find the -intercepts by eqauting .

and